please exsplain the j operator purpose and value?

Question

what exactly does the j operator represent what is the difference between for example j4 and -j4

Answer 1

j^2=i^2=-1. It is called an imaginary number (also known as a complex number) because you can not find it in the real world. It is really a way of simplifying problems in electrical engineering. The most widely use reason for imaginary numbers goes back to Euler's formula:e^x=cos(x)+sin(x)*j . It is a way of saying that a value contains a magnitude and an angle. It is hard to explain but easy to use when solving problems. You shouldn't need imaginary numbers until you get into differential equations.

Answer 2

As others have stated, j has the property j^2 = -1 or j = sqr(-1). It is called an imaginary number. We electrical engineers use j instead of i for this concept, probably because i represents current in most of our equations. In addition to Euler's Equation given by one of the previous answers, j is the imaginary unit for the imaginary part of a complex number of the form a + jb. The term b in this equation would be plotted along the imaginary axis on the complex plane while the a term would be plotted along the real axis. This whole concept introduces the notion of phasors, phase angles, magnitudes, etc for electrical signals as well as many other phenomenon that can be described elegantly in this fashion.

The difference between j4 and -j4 is the position on the complex plane and the resulting phase angle. As described, there is no real component and only an imaginary component. So j4 is positive and would have a magnitude of 4 and would lie on the imaginary axis above the real axis on the complex plane. It would have a phase angle of +90 degrees. -j4 would also have a magnitude of 4 and would also lie on the imaginary axis but would be below the real axis and would have a phase angle of -90 degrees. For electrical circuits, positive phase angles usually involve inductance, while negative phase angles usually imply capacitance. +j4 would represent a pure inductance while -j4 would represent a pure capacitance.

Carrying the example further, if the equations were 3 + j4 and 3 - j4, then the magnitude of each would be the same:

magnitude = sqr(real part ^2 + imaginary part ^2)
mag = sqr(3^2 + 4^2) = sqr(3^2 + (-4)^2) = sqr(9 + 16) = sqr(25) = 5
phase angle = arctan (imaginary part / real part)
3+j4 ==> arctan (+4 / 3) = +53.13 degrees
3-j4 ==> arctan (-4/3) = -53.13 degrees

Hope this helped!

Answer 3

The j operator in electrical engineering is used to represent the 90 deg phase component of ac signals and impedances. A multiplication by j means a phase angle change of 90 degrees. If you multiply by j twice, or j^2, you get a 180 degree phase shift which is the same as the negative of the original. Therefore j^2 = -1, and this is how we get j as the imaginary sqrt(-1).

Answer 4

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Answer 5

j is normally used to define imaginary numbers or current.

I'm not sure what your use is. If it's imaginary numbers then it means square root of -1.

If it's current, I need more information.

Answer 6

the - sign is a direction indicator.